Concept explainers
a)
To calculate: The probability for the range
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To calculate: The probability for the range
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To calculate: The probability for the range
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To calculate: The probability for the range
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Chapter 9 Solutions
Calculus: An Applied Approach (MindTap Course List)
- Let X be the number of minutes that it takes a random selected student to solve a mathematical problem. The probability density function of X is: 1) Find the probability that a student takes less than 1.5 minutes to solve themathematical problem.arrow_forwardA continuous random variable X has the probability density function f(x) so that f(x) is 0 for x≤≤≤≤0; f(x)=x for 0<x ≤ 1; f(x)= 2-x for 1<x≤ 2 and f(x) = 0 for x>2. Find the probability that X is at most 1/4.arrow_forwardA probability density function of a random variable is given by f(x)=x/8-1/2. on the interval [4,8] Find the median of the random variable, and find the probability that the random variable is between the expected value (mean) and the median.arrow_forward
- A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density functionarrow_forwardS2) The probability density function fX (x) of the random variable X fX(x) =( 4x3 0 < x ≤ 1 ( 0 otherwise given in the form. P(X ≤2/3|X > 1/3) Find the probability of the event.arrow_forwardA filling station recieves its supply of gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f(x) = 5*(1-x)4 for 0 less than or equal to x and x less than or equal to 1 and f(x) = 0 otherwise. Find the capacity of its tank so that the probability of its supply being exhausted in a given week is 10%arrow_forward
- distribution f(x) given-3 < x < -2 ------> c * x + 3 2 < x < 3 -------> 3 - c * x 0 elsewherefind the value of c so that f(x) is a valid probability density functionarrow_forwardAn electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.02 and fills are independent. Determine the probability mass function of the number of fills (x) before the manufacturing line is stopped.arrow_forwardMartian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. a)What is the probability that a Martian potato takes no more than 4 days to sprout? b) What is the probability that X >4? c) What is the probability that 2< X < 4? d) What is the expected value of X (E(X))? e) What is the expected value of X2 ? f) What is the variance of X? g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value? i) What is the expected value of X4 ? j) What is the probability that X is within 1 standard deviation of its expected value? k) What is the probability that X = .6?arrow_forward
- ~ The time to decay of an atom in a radioactive substance is a random variable X. The law of radioactive decay states that if N atoms arepresent at time t = 0, then N f (t) atoms will be present at time t, wheref(t) = e - kt (k > 0 is the decay constant). Explain the following statements:(b) The probability density function of Xis y = - f'(t).(c) The average time to decay is 1/ k.arrow_forwards) Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . . . , pn}. The entropyof the random variable is defined asH(X) = − Σn i=1 pi*log(pi)Find the probability mass function for the above discrete random variable that maximizes the entropy.arrow_forwardIn a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have a probability density function f(t) = 8 t 2 , t ≥ 8 where 8 seconds is the minimum time to traverse the maze. (a) Find the probability that an animal chosen at random takes between 28 and 56 seconds. (b) Find the probability that an animal chosen at random takes more than 28 seconds given that it took less than 56 seconds.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage